The default /etc/bash.bashrc (from the bash package) sources /etc/bash_completion (optionally from the bash-completion package) if it exists. The bash_completion script intern sources files in /etc/bash_completion.d/ if they exist. With Arch's git package a copy of /usr/share/git/completion/git-completion.bash ends up in the /etc/bash_completion.d/ directory. So, if you have the bash-completion package installed, completion for git should work automatically as soon as /etc/bash.bashrc is processed.